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Metric Characteristics of Hyperbolic Polygons and Polyhedra

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Abstract

In this paper, we consider some properties of hyperbolic polyhedra, both common with Euclidean and specific. Asymptotic behavior of metric characteristics of polyhedra in the n-dimensional hyperbolic space is examined in the cases where parameters of the polyhedra change and the dimension of the space unboundedly increases; in particular, the radius of the inscribed sphere of a polyhedron is estimated and its asymptotic behavior is obtained. In connection with this, the problem of estimating the minimal number of faces of the described polyhedron in the n-dimensional hyperbolic space depending on the radius of the inscribed sphere is posed. We also consider some properties of hyperbolic polygons that belong to both absolute geometry or only to hyperbolic geometry.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    E. A. Kostina

  2. Elabuga Institute (Branch) of the Kazan (Volga Region) Federal University, Elabuga, Russia

    N. N. Kostina

Authors
  1. E. A. Kostina
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  2. N. N. Kostina
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Correspondence to E. A. Kostina.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 169, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part II, 2019.

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Kostina, E.A., Kostina, N.N. Metric Characteristics of Hyperbolic Polygons and Polyhedra. J Math Sci 263, 379–386 (2022). https://doi.org/10.1007/s10958-022-05934-5

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  • DOI: https://doi.org/10.1007/s10958-022-05934-5

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